Our program is directed towards enlarging the understanding of macromolecular processes involved in control and regulation. We are concerned wtih the broad theoretical formulation of allosteric models and the precise experimental description of ligand linked allosteric phenomena. The respiratory proteins exhibit these properties in diverse ways and their study should lead to an understanding of their function in terms of structure and model processes. The primary approach is to perform precise thermodynamic measurements on ligand binding reactions and to analyze the results in terms of allosteric models. We are interested in linked reaction processes which involve multiple ligand (O2, CO, H+, DPG, electron) in terms of shifts in macromolecular conformations and states of aggregation. Precise binding and energetics reaction results form the basis of detailed characterization of such cooperative processes. The methods therefore involve a combination of specially developed experimental techniques now available (thin-layer spectrophotometric binding procedures, solution titration and gas reaction microcalorimetry, and small volume pH titrations), as well as techniques in development (spectrophotometric thin layer electron binding, steady-state photochemical ligand pumping, ligand binding in crystals). Specific problems include energetic of oxygen binding to heme proteins and hemocyanins, heats of sickle cell hemoglobin aggregation, and oxygen ligation in hemoglobin crystals. The interpretation of the concerned linkage processes is facilitated by formulation of appropriate partition functions in terms of allosteric and aggregated states of the system. Detailed computer simulation and data fitting procedures are employed in the analysis of results for specific systems. Interpretation of the thermodynamic results is enhanced by use of structural information through computer graphic display. Theoretical investigation of the mathematical properties of partition functions for simplified models provides general tests for their applicability to real systems.